The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1118,
author = {Ivan Chajda},
title = {Commutative directoids with sectional involutions},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {27},
year = {2007},
pages = {49-58},
zbl = {1133.06004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1118}
}
Ivan Chajda. Commutative directoids with sectional involutions. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 49-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1118/
[000] [1] I. Chajda and J. Kühr, A non-associative generalization of MV-algebras, Math. Slovaca, to appear. | Zbl 1150.06012
[001] [2] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69. | Zbl 0699.08002